Rule. "Multiply the breadth of the teeth by the square of the thickness, and divide the product by the length. The quotient will be the proportionate strength in horses' power, with a velocity of 2.27 feet per second. 66 By that rule I have calculated the following table; and, for the sake of comparison, I have taken three cases from Mr. Roberton's table, and three from your tables 3d and 5th. Explanation of the Table. "Column 2, contains the thickness of the teeth. The pitch is found by multiplying the thickness by 2.1*; and the length * That is in order to make the space between the teeth a little wider than the thickness of a tooth. See Art, 99, is found by multiplying the thickness by 1.2.* "Column 5, contains the proportionate strength, and also the number of horses' power (proportionate to the case H, see page 179), which the teeth is equal to, with a velocity of 2.27 feet per second. "1st, The last three cases in the table are taken from the tables 3d and 5th, and the results coincide so well with the co * Respecting the length of teeth, see Art. 103. lumns marked Z, that I presume the rule is just. 66 2dly, The first three cases are from Mr. Roberton's table; the second case is very near the same as in Mr. R's table; but the first is considerably less, and the third considerably more. Hence I infer that Mr. R. has taken his data from a pitch about three inches. "3dly, If any two wheels have the length and thickness of their teeth in the same proportion to their respective pitches, the breadth of the teeth and the velocity being the same, the strength will be directly as the pitches. The truth of this is deduced from the columns marked Z in tables 1st, 3d, and 5th. 102. TABLE OF PITCHES OF WHEELWORK, With the breadth and thickness of the teeth, and the corresponding strength in horses' power, calculated by Mr. CARMICHAEL'S rule. [A. 102.] It is not perhaps quite so difficult, as our author imagined, to determine, from first principles, the strength proper for teeth of wheels, and such a method must always be preferred to empirical rules. I shall here shew how to ap ply those principles which will give the reader an opportunity of comparing the two methods. In the first place let us consider under what circumstances the strain on a tooth will be the greatest possible. Let A B C D be the side of a tooth, then it will be evident, that the strain will be A D E B greatest, when the stress is thrown upon |